An algorithm for calculation parameters and cell size of detonation wave in a mixture of a gas with chemically inert microparticles is presented. Parameters of a steady detonation wave and detonation cell size in stoichiometric hydrogen-oxygen mixture with particles of W, Al2O3 and SiO2 are calculated. Results of calculations are used for analysis of the method of multifront detonation wave (DW) suppression by particles injection before the leading shock front. The ratio between the channel diameter and the detonation cell size is used to estimate the limit of detonation. The minimum total mass of the particles and the characteristic size of the cloud, which are necessary for detonation suppression, are calculated. It is shown, that such suppression is more effective, if the particles have high heat capacity, low melting point and high heat of melting. Among the particles under consideration the particles of Al2O3 are the best for DW suppression. Reflection of a steady one-dimensional detonation wave from a rigid wall in mixtures of a gas with chemically inert micro-particles has been considered. It is shown, that particles can essentially reduce pressure and temperature behind the reflected wave and therefore prevent crucial destruction of equipment, caused by detonation. An evolution of gaseous detonation wave structure in the cloud of chemically inert particles has been considered numerically. Different modes of detonation wave propagation behind the cloud have been analyzed and critical parameters of two-phase mixture, which are necessary for successful quenching of detonation, are calculated.